Question

What is x4-81 factored?

Answer 1

`x^4-81=(x^2)^2-9^2=(x^2-9)(x^2+9)=(x^2-3^2)(x^2+9)=\\\\=(x-3)(x+3)(x^2+9)`

Answer 2

What we need here:

"The difference of two squares is the same as (their sum) times (their difference)."

x^4 is the square of x² .
81 is the square of 9 .
Their difference is the same as (x² + 9) times (x² - 9).

But (x² - 9) is also the difference of two squares,
so it's the same thing as (x+ 3) times (x-3).

So the complete factored form of the original expression is

(x^4 - 81) = (x² + 9) (x+3) (x - 3)